To find the volume of a rectangular prism, we multiply the length, width, and height. In this case, the given information tells us that the base has an area of 15 square inches and the height is 5 inches.
Since the base is a rectangle, we know that its length multiplied by its width will give us an area of 15 square inches. Let's call the length of the base "l" and the width "w".
So, we have lw = 15.
We also know that the height of the box is 5 inches.
To find the volume, we multiply the length, width, and height:
volume = lw * h.
Substituting in the values we know:
volume = 15 * 5.
Simplifying:
volume = 75.
Therefore, the volume of the gift box is 75 cubic inches. Answer: \boxed{75}.
Question
A gift box is being constructed in the shape of a right rectangular prism. The base is 15 inches squared and the height is 5 inches. What will the volume of the gift box be?(1 point)
in.3
7 answers
What is the volume of a rectangular pyramid with a length of 32 cm, a width of 25 cm, and an altitude of 41 cm?(1 point)
Responses
32.67 cm3
32.67 cm cubed
32,800 cm3
32,800 cm cubed
98,400 cm3
98,400 cm cubed
10,933.33 cm3
Responses
32.67 cm3
32.67 cm cubed
32,800 cm3
32,800 cm cubed
98,400 cm3
98,400 cm cubed
10,933.33 cm3
To find the volume of a rectangular pyramid, we multiply the base area by the height and divide by 3.
The given information tells us that the length of the base is 32 cm, the width of the base is 25 cm, and the altitude (height) is 41 cm.
To find the base area, we multiply the length and width:
base area = length * width = 32 cm * 25 cm = 800 cm^2.
Now, we can calculate the volume of the pyramid:
volume = (base area * height) / 3
volume = (800 cm^2 * 41 cm) / 3
volume = 32,800 cm^3.
Therefore, the volume of the rectangular pyramid is 32,800 cm^3. Answer: \boxed{32,800}.
The given information tells us that the length of the base is 32 cm, the width of the base is 25 cm, and the altitude (height) is 41 cm.
To find the base area, we multiply the length and width:
base area = length * width = 32 cm * 25 cm = 800 cm^2.
Now, we can calculate the volume of the pyramid:
volume = (base area * height) / 3
volume = (800 cm^2 * 41 cm) / 3
volume = 32,800 cm^3.
Therefore, the volume of the rectangular pyramid is 32,800 cm^3. Answer: \boxed{32,800}.
A resort is building a scuba diving lagoon in the shape of an upside down pyramid. The top of the lagoon is a rectangle that is 50 feet by 20 feet, and the deepest point of the lagoon is in the middle at 25 feet deep. How much water does the lagoon hold?(1 point)
Responses
95 ft.3
95 feet cubed
25,000 ft.3
25,000 feet cubed
8,333.33 ft.3
8,333.33 feet cubed
75,000 ft.3
75,000 feet cubed
Responses
95 ft.3
95 feet cubed
25,000 ft.3
25,000 feet cubed
8,333.33 ft.3
8,333.33 feet cubed
75,000 ft.3
75,000 feet cubed
To find the volume of an upside-down pyramid, we need to find the total volume of each layer of the pyramid and then add them together.
The given information tells us that the top of the lagoon is a rectangle with dimensions 50 feet by 20 feet. The depth of the lagoon at the deepest point, which is in the middle, is 25 feet.
The first step is to find the volume of the rectangular top layer. The formula for the volume of a rectangular prism is length * width * height. In this case, the length is 50 feet, the width is 20 feet, and the height is 25 feet (since that is the depth of the lagoon at the deepest point).
Volume of top layer = 50 ft * 20 ft * 25 ft = 25,000 ft^3.
Next, we need to find the volume of the layer below the top layer. Since the lagoon is in the shape of an upside-down pyramid, the dimensions of this layer will be half of the top layer. So, the length will be 50 feet, the width will be 20 feet, and the height will be 25 feet.
Volume of second layer = (50 ft * 20 ft * 25 ft) / 2 = 12,500 ft^3.
Finally, we add the volumes of the two layers together to find the total volume of the lagoon:
Total volume = 25,000 ft^3 + 12,500 ft^3 = 37,500 ft^3.
Therefore, the lagoon holds 37,500 ft^3 of water. Answer: \boxed{37,500}.
The given information tells us that the top of the lagoon is a rectangle with dimensions 50 feet by 20 feet. The depth of the lagoon at the deepest point, which is in the middle, is 25 feet.
The first step is to find the volume of the rectangular top layer. The formula for the volume of a rectangular prism is length * width * height. In this case, the length is 50 feet, the width is 20 feet, and the height is 25 feet (since that is the depth of the lagoon at the deepest point).
Volume of top layer = 50 ft * 20 ft * 25 ft = 25,000 ft^3.
Next, we need to find the volume of the layer below the top layer. Since the lagoon is in the shape of an upside-down pyramid, the dimensions of this layer will be half of the top layer. So, the length will be 50 feet, the width will be 20 feet, and the height will be 25 feet.
Volume of second layer = (50 ft * 20 ft * 25 ft) / 2 = 12,500 ft^3.
Finally, we add the volumes of the two layers together to find the total volume of the lagoon:
Total volume = 25,000 ft^3 + 12,500 ft^3 = 37,500 ft^3.
Therefore, the lagoon holds 37,500 ft^3 of water. Answer: \boxed{37,500}.
A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work.
The formula for the volume of a pyramid is V = (1/3) * base area * height.
We are given that the length of the pyramid is 7 cm and the width is 9 cm. Let's call the height of the pyramid "h", and we can calculate the base area using the length and width.
The base area is given by: base area = length * width = 7 cm * 9 cm = 63 cm^2.
We are also given that the volume of the pyramid is 231 cubic centimeters.
We can substitute the known values into the volume formula and solve for the height:
231 cm^3 = (1/3) * 63 cm^2 * h.
Multiplying both sides of the equation by 3 to get rid of the fraction:
3 * 231 cm^3 = 63 cm^2 * h.
Simplifying:
693 cm^3 = 63 cm^2 * h.
Now, we can isolate h by dividing both sides of the equation by 63 cm^2:
h = 693 cm^3 / 63 cm^2.
Simplifying:
h = 11 cm.
Therefore, the height of the pyramid is 11 cm. Answer: \boxed{11}.
We are given that the length of the pyramid is 7 cm and the width is 9 cm. Let's call the height of the pyramid "h", and we can calculate the base area using the length and width.
The base area is given by: base area = length * width = 7 cm * 9 cm = 63 cm^2.
We are also given that the volume of the pyramid is 231 cubic centimeters.
We can substitute the known values into the volume formula and solve for the height:
231 cm^3 = (1/3) * 63 cm^2 * h.
Multiplying both sides of the equation by 3 to get rid of the fraction:
3 * 231 cm^3 = 63 cm^2 * h.
Simplifying:
693 cm^3 = 63 cm^2 * h.
Now, we can isolate h by dividing both sides of the equation by 63 cm^2:
h = 693 cm^3 / 63 cm^2.
Simplifying:
h = 11 cm.
Therefore, the height of the pyramid is 11 cm. Answer: \boxed{11}.
1 answer